Abstract
AbstractWe review the notions of symplectic and orthogonal vector bundles over curves, and the connection between principal parts and extensions of vector bundles. We give a criterion for a certain extension of rank 2n to be symplectic or orthogonal. We then describe almost all of its rank n vector subbundles using graphs of sheaf homomorphisms, and give criteria for the isotropy of these subbundles. Finally, we sketch the use of these ideas in moduli questions for symplectic vector bundles. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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